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MHT CET · Physics · Kinetic Theory of Gases

A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in changing the internal energy is

  1. A \(30 \%\)
  2. B \(40 \%\)
  3. C \(50 \%\)
  4. D \(60 \%\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(60 \%\)

Step-by-step Solution

Detailed explanation

For a monoatomic gas,
\(\gamma=\frac{C_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{5}{3}\)
We know \(\Delta \mathrm{Q}=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{T}\) and \(\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{v}} \Delta \mathrm{T}\)
\(\frac{\Delta U=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{~T}}{\Delta \mathrm{Q}=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{~T}}=\frac{\mathrm{C}_{\mathrm{V}}}{\mathrm{C}_{\mathrm{P}}}=\frac{3}{5}\)
\(\therefore \quad\) The percentage of total heat used in changing the internal energy is \(\frac{3}{5} \times 100=60 \%\).